### ekm507's blog

By ekm507, 7 years ago, I'll tell you about an amazing number:6174.

more than 60 years ago in 1950 a mathematician called "Kaprekar" found an amazing relation between 6174 and four digit numbers.

I'll show you what it was.

Consider a four digit number which doesn't have 3 or 4 digits duplicate. for example you can consider 2325 or 6565 or 1234. but you can't consider 7777 or 2232 now you will heave the digits and make biggest and smallest number. for example if you have considered 4510 you will make 5410 and 145. then subtract the small number from the big number, for this example:

4510 --> 5410-145=5265

for obtained number repeat previous steps. after some steps you will reach to number:6174. For example:

4510 --> 5410-145=5265

5265 --> 6552-2556=3996

3996 --> 9963-3699=6264

6264 --> 6642-2466=4176

4176 --> 7641-1467=6417 ((you have reached 6417.))

as you know for 4176:

6174 --> 7641-1467=6417

I think that's amazing.

Another example:

2015

2015 --> 5210-125=5085

5085 --> 8550-558=7992

7992 --> 9972-2799=7173

7173 --> 7731-1377=6354

6354 --> 6543-3456=3087

3087 --> 8730-378=8352

8352 --> 8532-2358=6174 ((you have reached 6174.))

This was what "Kaprekar" had found it in 1950.

Good luck ^_^ 